This invention relates to modulation systems for sending digital data via a channel.
Considerable progress has been made in recent years towards approaching the channel capacity of ideal bandlimited Gaussian channels using coded modulation. Ideal Gaussian channels have flat spectra and additive white Gaussian noise.
On ideal Gaussian channels, when the signal-to-noise ratio (SNR) is large, or equivalently when the number of bits per symbol becomes large, the difference between channel capacity and what can be achieved with uncoded modulation systems such as uncoded quadrature amplitude modulation (QAM) is about 9 dB, at error rates of the order of 10.sup.-5 -10.sup.-6 (Forney, et al., "Efficient Modulation for Band-limited Channels," IEEE J. Select. Areas Commun., vol. SAC 2, pp. 632-647, 1984, incorporated by reference). Known coded modulation schemes can achieve effective `coding gains` of the order of 6 dB, largely closing this gap.
Effective coded modulation schemes for the ideal bandlimited Gaussian channel use lattice codes or lattice-type trellis codes, both of which may be considered as coset codes "Coset Codes--Part I: Introduction and Geometrical Classification," IEEE Trans. Inform. Theory, vol. IT-34, Sep., 1988, incorporated by reference. It has been recognized that, with such codes, the coding gain may be separated into two parts, a `fundamental coding gain` due to the underlying coset code, and a `shape gain` due to the shape of the signal constellation boundary.
Codes such as Ungerboeck's one-dimensional and two-dimensional lattice type trellis codes (Ungerboeck, "Channel Coding with Multilevel/Phase Signals", IEEE Transactions on Information Theory, Vol. IT-28, pp. 55-67, Jan., 1982) or Wei's multidimensional codes (L-F. Wei, "Trellis-coded modulation with multidimensional constellations," IEEE Trans. Inform. Theory, Vol. IT-33, pp. 483-501, 1987, incorporated by reference) can achieve fundamental coding gains of up to 6 dB, or effective coding gains of the order of 5 dB, if the effects of `error coefficient` are taken into account (Forney, "Coset Codes", supra).
The `shape gain` measures the improvement due to the shape of the constellation boundary compared to the square boundary which is commonly employed in simple QAM constellations. If shaping results in a spherical signal constellation boundary in higher dimensions, or equivalently in an effective Gaussian distribution in two-dimensions, then shape gains up to a factor of .pi.e/6 (1.53 dB) can be attained (Forney, et al., supra). On ideal channels, it has been shown that shape gains in excess of 1 dB can be achieved using Voronoi constellations as disclosed in Forney, U.S. patent application Ser. No. 062,497, filed Jun. 12, 1987, and Forney, U.S. patent application Ser. No. 181,203, filed Apr. 13, 1988, or using trellis shaping as disclosed in Forney and Eyuboglu, Trellis Shaping for Modulation Systems, U.S. patent application Ser. No. 312,254, filed Feb. 16, 1989, all incorporated by reference.
In general, coded modulation schemes are designed for ideal channels and practical trellis coded modulation schemes can achieve coding gains of up to the order of 6 dB, thus largely closing the gap to capacity. This coding gain may be viewed as the combination of a fundamental coding gain of the order of 5 dB (effective) and a shape gain of the order of 1 dB.
For non-ideal channels exhibiting non-flat spectra and white noise, linear equalization techniques are conventionally used to create an equalized channel which is as ideal as possible. Linear equalizers are effective if the intersymbol interference (ISI) is not too severe, but when the channel has nulls or near nulls, as is always the case when we wish to use the greatest practical bandwidth on a bandlimited channel, then linear equalization techniques suffer excessive noise enhancement. Similarly, on non-ideal channels with flat response where the noise spectrum is non-flat, linear equalization cannot effectively exploit the correlation in the noise signal. More generally, on channels where the SNR spectrum exhibits large variations within the signal band, a linear equalizer may not perform adequately.
For uncoded systems, two known schemes which can substantially outperform linear equalizers on channels with severly distorted SNR spectra are decision-feedback equalization (DFE) and generalized precoding. A so-called conventional DFE eliminates noise correlation and `pre-cursor` ISI using a linear filter, and cancels `post-cursor` ISI using prior decisions. With generalized precoding, sometimes called `decision feedback in the transmitter`, a comparable effect is achieved by a subtraction in the transmitter, using modulo arithmetic. Generalized precoding, unlike DFE, requires knowledge of the channel response in the transmitter, but, also unlike DFE, is not susceptible to error propagation.
It has been shown that at high SNR's the channel capacity can be approached by combining coded modulation schemes designed for ideal channels with ideal (correct feedback) zero-forcing DFE (Price, "Nonlinearly feedback-equalized PAM versus capacity for noisy filter channel," ICC Conf. Record, pp 22-12 to 22-17 1972; and Eyuboglu, "Detection of Severly Distorted Signals Using Decision Feedback Noise Prediction with Interleaving," IEEE Trans. Commun., vol. COM-36, pp. 401-409, Apr., 1988, both incorporated by reference). Indeed, at high SNR's the dB gap between uncoded QAM with DFE and the channel capacity is also 9 dB at error rates of the order of 10.sup.-5 -10.sup.-6. Unfortunately, for coded systems, it is not possible to use DFE directly because decisions made with no delay are unreliable. Several methods for approaching DFE performance with coded systems have been proposed (see U.S. Pat. Nos. 4,631,735, and 4,713,829 issued Mar. 26, 1985 and Jun. 19, 1985, respectively). One of these, reduced-state sequence estimation (RSSE), can approach the performance of maximum likelihood sequence estimation (MLSE), at greatly reduced complexity. The simplest version of RSSE, called parallel decision feedback decoding (PDFD), is closely related to DFE.
Generalized precoding for coded systems is disclosed in our copending U.S. patent application Ser. No. 208,867, entitled Partial Response Channel Signaling Systems, filed Jun. 15, 1988, incorporated by reference. These applications discuss non-ideal partial response channels with responses of the form h(D)=1.+-.D.sup.n. With generalized precoding, for large bits/symbol, essentially the same coding gains (relative to an uncoded system with ideal DFE) can be obtained with the same code and the same decoding complexity over any non-ideal channel as can be obtained over an ideal channel except for the shaping gain, if the channel response is known in the transmitter.